代数

图书标准信息

• 作者 Algebra Revised Third Edition 著
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 1
• ISBN 9787506271844
• 定价 126.00元
• 装帧 精装
• 开本 24开
• 纸张 胶版纸
• 页数 914页

【内容简介】

　　AsIseeit，thegraduatecourseinalgebramustprimarilypreparestudentstohandlethealgebrawhichtheywillmeetinallofmathematics：topology，partialdifferentialequations，differentialgeometry，algebraicgeometry，analysis，andrepresentationtheory，nottospeakofalgebraitselfandalgebraicnumbertheorywithallitsramifications.HenceIhaveinsertedthroughoutreferencestopapersandbookswhichhaveappearedduringthelastdecades，toindicatesomeofthedirectionsinwhichthealgebraicfoundationsprovidedbythisbookareused;Ihaveaccompaniedthesereferenceswithsomemotivatingcomments，toexplainhowthetopicsofthepresentbookfitintothemathematicsthatistocomesubsequentlyinvariousfields;andIhavealsomentionedsomeunsolvedproblemsofmathematicsinalgebraandnumbertheory.Theabcconjectureisperhapsthemostspectacularofthese.

【目录】

PartOneTheBasicObjectsofAlgebra
Chapter1Groups
1.Monoids
2.Groups
3.Normalsubgroups
4.Cyclicgroups
5.Operationsofagrouponaset
6.Sylowsubgroups
7.Directsumsandfreeabeliangroups
8.Finitelygeneratedabeliangroups
9.Thedualgroup
10.Inverselimitandcompletion
11.Categoriesandfunctors
12.Freegroups
Chapter2Rings
1.Ringsandhomomorphisms
2.Commutativerings
3.Polynomialsandgrouprings
4.Localization
5.Principalandfactorialrings
Chapter3Modules
Chapter4Polynomlals
PartTwoAlgebraicEquations
Chapter5AlgebralcExtensions
Chapter6GaloisTheory
Chapter7ExtensionsofRings
Chapter8TranscendentalExtensions
Chapter9AlgebraicSpaces
Chapter10NoetherialRingsandModules
Chapter11RealFields
Chapter12AbsoluteValues
PartThreeLiearAlebarandReqresentations
Chapter13MatricesandLinearMaps
Chapter14RepresentatlonofOneEndomorphism
Chapter15StructureofBilinearForms
Chapter16TheTensorProduct
Chapter17Smisimplicity
Chapter18RepresentationsofFiniteGroups
Chapter19TheAlternatingProduct
PartFourHomologicalAlgebra
Chapter20GeneralHomologyTheory
Chapter21FiniteFreeResolutions
Appendix1TheTranscendenceofeand
Appendix2SomeSetTheory
Bibliography
Index